Most efficient way to repeat a cutout pattern
One way to do this is with a radial Array Modifier (read about it here: How to make a circular array using offset object as center? ) and a Boolean Modifier or the Booltool add-on.
first, for convenience, put your round cylinder thing right in the middle of your scene.

Then put a little cylinder, the size of one of the little holes, on the edge of your big cylinder (make sure it sticks al the way though). In exactly the same spot, put an Empty (can be any Empty or Object). In the image I used a Plain Axes.

Now put an Array Modifier on the little cylinder. Put in the right a number of cylinders in the Count field (just put 100 first and adjust it later).
Uncheck all the Offset boxes, but check the Object Offset box. As a target, choose the empty.
Then make sure the Transform Pivot Point (here at the bottom of the image) is set to 3D Cursor. Press Shift + C to put the 3D cursor in the middle of your scene, and because you put the big cylinder there, in the middle of the big cylinder.
Then rotate the empty on the z-axis. (I think you will need only a fraction of a degree)

Then duplicate your tiny cylinder and go into Edit Mode. Move it a little bit down and a little bit to the side (to get your alternating circle cutout pattern).

Activate the Booltool add-on in the Preferences window.
Select the cylinder array, and then shift select the big cylinder. With both objects selected, choose Difference.

Then hide or delete the cylinder array.
Result with three arrays:

If you want less holes, apply the Array Modifier, and delete the holes you don't want before using Booltool
You can also apply the Array Modifier to two rows of tiny cylinders, make them one object by selecting them both and pressing Ctrl + J. And then put another new Array Modifier on the new combined object with a Constant Offset or Relative Offset in the z-axis direction. And then do the Booltool actions.